CPSO: Chaotic Particle Swarm Optimization for Cluster Analysis

Background:To solve the cluster analysis better,we propose a new method based on the chaotic particle swarm optimization(CPSO)algorithm.Methods:In order to enhance the performance in clustering,we propose a novel method based on CPSO.We first evaluate the clustering performance of this model using the variance ratio criterion(VRC)as the evaluation metric.The effectiveness of the CPSO algorithm is compared with that of the traditional particle swarm optimization(PSO)algorithm.The CPSO aims to improve the VRC value while avoiding local optimal solutions.The simulated dataset is set at three levels of overlapping:non-overlapping,partial overlapping,and severe overlapping.Finally,we compare CPSO with two other methods.Results:By observing the comparative results,our proposed CPSO method performs outstandingly.In the conditions of non-overlapping,partial overlapping,and severe overlapping,our method has the best VRC values of 1683.2,620.5,and 275.6,respectively.The mean VRC values in these three cases are 1683.2,617.8,and 222.6.Conclusion:The CPSO performed better than other methods for cluster analysis problems.CPSO is effective for cluster analysis.

Image Thresholding Using Two-Dimensional Tsallis Cross Entropy Based on Either Chaotic Particle Swarm Optimization or Decomposition

The segmentation effect of Tsallis entropy method is superior to that of Shannon entropy method, and the computation speed of two-dimensional Shannon cross entropy method can be further improved by optimization. The existing two-dimensional Tsallis cross entropy method is not the strict two-dimensional extension. Thus two new methods of image thresholding using two-dimensional Tsallis cross entropy based on either Chaotic Particle Swarm Optimization (CPSO) or decomposition are proposed. The former uses CPSO to find the optimal threshold. The recursive algorithm is adopted to avoid the repetitive computation of fitness function in iterative procedure. The computing speed is improved greatly. The latter converts the two-dimensional computation into two one-dimensional spaces, which makes the computational complexity further reduced from O(L2) to O(L). The experimental results show that, compared with the proposed recently two-dimensional Shannon or Tsallis cross entropy method, the two new methods can achieve superior segmentation results and reduce running time greatly.

Optimal Operation of Energy Internet Based on User Electricity Anxiety and Chaotic Spatial Variation Particle Swarm Optimization

Ignoring load characteristics and not considering user feeling with regard to the optimal operation of Energy Internet（EI） results in a large error in optimization. Thus, results are not consistent with the actual operating conditions. To solve these problems, this paper proposes an optimization method based on user Electricity Anxiety（EA） and Chaotic Space Variation Particle Swarm Optimization（CSVPSO）. First, the load is divided into critical load, translation load, shiftable load, and temperature load. Then, on the basis of the different load characteristics,the concept of the user EA degree is presented, and the optimization model of the EI is provided. This paper also presents a CSVPSO algorithm to solve the optimization problem because the traditional particle swarm optimization algorithm takes a long time and particles easily fall into the local optimum. In CSVPSO, the particles with lower fitness value are operated by using cross operation, and velocity variation is performed for particles with a speed lower than the setting threshold. The effectiveness of the proposed method is verified by simulation analysis.Simulation results show that the proposed method can be used to optimize the operation of EI on the basis of the full consideration of the load characteristics. Moreover, the optimization algorithm has high accuracy and computational efficiency.

A GPS/BDS dual-mode positioning algorithm for a train based on CIPSO_EKF

When using global positioning system/BeiDou navigation satellite(GPS/BDS)dual-mode navigation system to locate a train,Kalman filter that is used to calculate train position has to be adjusted according to the features of the dual-mode observation.Due to multipath effect,positioning accuracy of present Kalman filter algorithm is really low.To solve this problem,a chaotic immune-vaccine particle swarm optimization_extended Kalman filter(CIPSO_EKF)algorithm is proposed to improve the output accuracy of the Kalman filter.By chaotic mapping and immunization,the particle swarm algorithm is first optimized,and then the optimized particle swarm algorithm is used to optimize the observation error covariance matrix.The optimal parameters are provided to the EKF,which can effectively reduce the impact of the observation value oscillation caused by multipath effect on positioning accuracy.At the same time,the train positioning results of EKF and CIPSO_EKF algorithms are compared.The eastward position errors and velocity errors show that CIPSO_EKF algorithm has faster convergence speed and higher real-time performance,which can effectively suppress interference and improve positioning accuracy.

Recognition of motor imagery tasks for BCI using CSP and chaotic PSO twin SVM

Accurate modeling and recognition of the brain activity patterns for reliable communication and interaction are still a challenging task for the motor imagery （MI） brain-computer interface （BCI） system. In this paper, we propose a common spatial pattern （CSP） and chaotic particle swarm optimization （CPSO） twin support vector machine （TWSVM） scheme for classification of MI electroencephalography （EEG）. The self-adaptive artifact removal and CSP were used to obtain the most distinguishable features. To improve the recognition results, CPSO was employed to tune the hyper-parameters of the TWSVM classifier. The usefulness of the proposed method was evaluated using the BCI competition IV-IIa dataset. The experimental results showed that the mean recognition accuracy of our proposed method was increased by 5.35%, 4.33%, 0.78%, 1.45%, and 9.26% compared with the CPSO support vector machine （SVM）, particle swarm optimization （PSO） TWSVM, linear discriminant analysis （LDA）, back propagation （BP） and probabilistic neural network （PNN）, respectively. Furthermore, it achieved a faster or comparable central processing unit （CPU） running time over the traditional SVM methods.

Neuro-optimized numerical treatment of HIV infection model

In this paper,a neuro-optimized numerical method is presented for approximation of HIV virus progression model in the human body.The model is composed of coupled nonlinear system of differential equations(DEs)containing healthy and infected T-Cells and HIV free virus particles.The coupled system is transformed into feedforward artificial neural network(ANN)with Mexican hat wavelet function in the hidden layers.Two meta-heuristic algorithms based on chaotic particle swarm optimization(CPSO)and its hybrid version with local search technique are exploited to tune the parameters of ANN in an unsupervised manner of error function.A comprehensive testbed is established to observe the virus growth per day with performance metric containing fitness value,computational time complexity and convergence.The proposed solutions are compared with state of art Runge-Kutta method and Legendre Wavelet Collocation Method(LWCM).The core advantages of the proposed scheme are getting the solution on continuous grid,consistent convergence,simplicity in implementation and handling strong nonlinearity effectively.

Near Optimal PID Controllers for the Biped Robot While Walking on Uneven Terrains

The execution of the gaits generated with the help of a gait planner is a crucial task in biped locomotion. This task is to be achieved with the help of a suitable torque based controller to ensure smooth walk of the biped robot. It is important to note that the success of the developed proportion integration differentiation （PID） controller depends on the selected gains of the controller. In the present study, an attempt is made to tune the gains of the PID controller for the biped robot ascending and descending the stair case and sloping surface with the help of two non-traditional optimization algorithms, namely modified chaotic invasive weed optimization （MCIWO） and particle swarm optimization （PSO） algorithms. Once the optimal PID controllers are developed, a simulation study has been conducted in computer for obtaining the optimal tuning parameters of the controller of the biped robot. Finally, the optimal gait angles obtained by using the best controller are fed to the real biped robot and found that the biped robot has successfully negotiated the said terrains.